As @Swamidass eloquently outlines, looking at human variation alone doesn’t grant a miraculous bottleneck anytime in the past 500 kya (looking at TMR4A). But really, the idea of TMR4A is rather ridiculous from a purely scientific perspective. Not that the idea itself is not scientifically sound, it very much is and can be calculated, but you would never have two individuals that have two alleles at every loci that are different from their spouse and thus the timeliness of such a bottleneck (if there was one) would be even further in the past. Hence its more likely that a bottleneck (if there was one) would be closer to the average TMRCA.
But that’s only looking at human variation, not any kind of trans species evidence like shared polymorphisms or incomplete lineage sorting which also provide population estimates of populations and at least the latter do not reveal any bottlenecks at all going back much further.